In the calibration of a precision acoustic sensor, the signal response R(s)R(s)R(s) for a sensitivity parameter s s\,s is modeled by the function
R(s)=(2+ks4)5R(s) = \left( 2 + \frac{ks}{4} \right)^5R(s)=(2+4ks)5
where k k\,k is a non-zero constant.
Find the first 4 terms, in ascending powers of sss, of the binomial expansion of R(s)R(s)R(s). Give each term in its simplest form.
An enhanced signal model is defined by
G(s)=(5+2s)(2+ks4)5G(s) = (5 + 2s) \left( 2 + \frac{ks}{4} \right)^5G(s)=(5+2s)(2+4ks)5
In the series expansion of G(s)G(s)G(s), the coefficient of s s\,s is equal to the constant term. Find the value of kkk.
Practise Edexcel A Level Maths Binomial Expansion with exam-style questions for A Level Maths. 100 questions covering 4.1 Expanding (1 + x)^n, 4.2 Expanding (a + bx)^n, and 4.3 Using Partial Fractions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.